Reserve 8 ginger slices for garnish. Place the rest in a small saucepan with the maple syrup, and bring to a slow simmer over medium-low heat. Cook for 10 minutes. Let cool at room temperature for about 1 hour.
Strain the cooled maple syrup mixture into a large liquid measuring cup, press on the ginger with a wooden spoon or spatula to extract as much flavor as possible, then discard the ginger. Stir in the lemon juice and vodka.
To serve, fill 4 tall glasses with ice. Divide the lemonade mixture among them, and top with the club soda. Garnish each glass with 2 reserved ginger slices and serve immediately.
Put the brown sugar in a small saucepan, stir in 1 cup water and bring to a simmer over medium heat. Cook, stirring occasionally, until the sugar dissolves, about 5 minutes. Cool completely before using.
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